What is a Line? A line is the set of points forming a straight path on a plane The slant (slope) between any two points on a line is always equal A line.

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Presentation transcript:

What is a Line? A line is the set of points forming a straight path on a plane The slant (slope) between any two points on a line is always equal A line on the Cartesian plane can be described by a linear equation x-axis y-axis

Definition - Linear Equation Any equation that can be put into the form Ax + By  C = 0, where A, B, and C are Integers and A and B are not both 0, is called a linear equation in two variables. The graph will be a straight line. The form Ax + By  C = 0 is called standard form (Integer coefficients all on one side = 0)

Definition - Linear Equation The equation of a line describes all of the points on the line The equation is the rule for any ordered pair on the line 1.3x + 2y – 8 = 0 (4, -2) is on the line (5, 1) is not on the line 2.x – 7y + 2 = 0 (4, -2) is not on the line (5, 1) is on the line Examples: Test the point by plugging the x and y into the equation

Slope Slope describes the direction of a line.

x-axis y-axis Find the slope between (-3, 6) and (5, 2) Rise Run == (-3, 6) (5, 2)

Calculate the slope between (-3, 6) and (5, 2) x 1 y 1 x 2 y 2 We use the letter m to represent slope m

Find the Slopes (5, -2) (11, 2) (3, 9) Yellow Blue Red

Find the slope between (5, 4) and (5, 2). STOP This slope is undefined. x 1 y 1 x 2 y 2

x y Find the slope between (5, 4) and (5, 2). Rise Run -2 0 Undefined ==

Find the slope between (5, 4) and (-3, 4). This slope is zero. x 1 y 1 x 2 y 2

x y Rise Run 0 -8 Zero == Find the slope between (5, 4) and (-3, 4).

From these results we can see... The slope of a vertical line is undefined. The slope of a horizontal line is 0.

Find the slope of the line 4x  y = 8 Here is an easier way Solve for y. When the equation is solved for y the coefficient of the x is the slope. We call this the slope-intercept form y = mx + b m is the slope and b is the y-intercept

x y Graph the line that goes through (1, -3) with (1,-3)

Sign of the Slope Which have a positive slope? Green Blue Which have a negative slope? Red Light Blue White Undefined Zero Slope